Above My Pay Grade......

[Mike Truran]

The white Queen decides to throw a party and invites the white pieces only. The party is to be held on the chess board which has 64 places for guests. There are no pawns invited. The white King thinks it is a bit mean to only have eight at the party and suggests that the Black King and Queen should also be invited. The White Queen says that there is really no room as the other 56 seats are 'covered' and any Black piece attending will be 'at risk of capture'. Is the Queen right and if she is what does the seating plan look like?

[John Upham]

If the 64 squares are for guests then presumably the white queen will be skipping the party.

[IanCalvert]

Is the Queen right and if she is what does the seating plan look like?

Yes: a simple greedy algorithm works.

Q on g2
Rooks on f1 and h3 .

This reduces possible squares for Black pieces to a 5x5 area.

Knights on c7 and c6 to take as many squares as possible of that 5x5 area.

Similarly bishops on c8 and c5.

King on b5.

[Stewart Reuben]

I prefer this position.
Qh1, Rg1, Rh2, Bf1, Bg3, Nf2, Nh3, Kg2.
Black ke3, qf3. Those two black gate-crashers might prove to be rather unwelxome.
Of course John Upham is quite right. Moreover, there are only 7 guests.

The problem of course is what Mike meant originally. Did he mean that the chosen placement of the 8 White pieces meant that the Black queen and king are under threat? If so, then Ian Calvert's ingenious solution is quite correct for ANY Black piece, but not both k and q as the queen can shield the king. For example, there can be kf5 or kf6 and qf5. Or kd2 and qe2+

But perhap he meant that it is possible to construct a position of the 8 White pieces such that, wherever the Black king and Black queen are placed, BOTH are under threat.
Constructing such a position is certainly above my pay grade. Unless...
White pawns could have been promoted to other pieces, e.g. It would be possible to have 7 White queens and the king. There are still no pawns. Mike didn't even say the position had to be legal. So both kings could be touching or both be in check, or there be no previous legal move.
There are now so many possibilities, my mind boggles.